# Advance Math Series 2000 Important Questions Mensuration Part 14

**Advance Math Series 2000 Important Questions Mensuration Part 14**

**Advance Math Series 2000 Important Questions Mensuration Part 14**

**Q1042. A copper wire of length 36 m and diameter 2 mm is melted to form a sphere. The radius of the sphere (in cm) is**

(a) 2.5 (b) 3 (c) 3.5 (d) 4

**Q1043.A child reshapes a cone made up of clay of height 24cm and radius 6 cm into a sphere. The radius (in cm) of the sphere is **

(a) 6 (b) 12 (c) 24 (d) 48

**Q1044. The total surface area of a solid right circular cylinder is twice that of a solid sphere. If they have the same radii, the ratio of the volume of the cylinder to that of the sphere is given by**

(a) 9 : 4 (b) 2 : 1 (c) 3 : 1 (d) 4 : 9

**Q1045. Water is flowing at the rate of 3 km/hr through a circular pipe of 20 cm internal diameter into a circular cistern of diameter 10m and depth 2m. In how much time will the cistern be filled?**

(a) 1 hour (b) 1 hour 40 minutes (c) 1 hour 20 minutes (d) 2 hours 40 minutes

**Q1046.Marbles of diameter 1.4 cm are dropped into a cylindrical beaker containing some water and are fully submerged. The diameter of the beaker is 7 cm. Find how many marbles have been dropped in it, if the water rises by 5.6 cm.**

(a) 50 (b) 150 (c) 250 (d) 350

**Q1047.A solid metallic sphere of radius 8 cm is melted to form 64 equal small solid spheres. The ratio of the surface area of this sphere to that of a small sphere is**

(a) 4 : 1 (b) 1 : 16 (c) 16 : 1 (d) 1 : 4

**Q1048.The areas of three consecutive faces of a cuboid are 12 cm ^{2}, 20 cm^{2} and 15 cm^{2}, then the volume (in cm^{3}) of the cuboid is**

(a) 3600 (b) 100 (c) 80 (d) 60

**Q1049.The sides of a triangle are in the ratio 2 : 3 : 4. The perimeter of the triangle is 18 cm. The area (in cm ^{2}) of the triangle is **

(a) 9 (b) 36 (c) (d) 3

**Q1050.if a wire is bent into the shape of a square, then the area of the, square so formed is 81 cm ^{2}. When the wire is rebent into a semicircular shape, then the area. (in cm^{2}) of the semi circle will be(Take π =22/7)**

(a) 22 (b) 44 (c) 77 (d) 154

**Q1051.If the radius of a circle is increased by 50%, its area is increased by**

(a) 125% (b) 100% (c) 75% (d) 50%

**Q1052.A hemisphere and a cone have equal bases. If their heights are also equal, the ratio of their curved surfaces will be**

(a) 1 :√2 (b) √2 : 1 (c) 1 : 2 (d) 2 : 1

**Q1053.The floor of a room is of size 4m × 3m **** and its height is 3m. The walls and ceiling of the room require painting. The area to be painted is **

(a) 66m^{2} (b) 54m^{2} (c) 43m^{2} (d) 33m^{2}

**Q1054.In an equilateral triangle ABC of side 10 cm, the side BC is trisected at D, Then the length (in cm) of AD is**

(a) 3√3 (b) 7√3 (c) 10√7/3 (d)7√10/3

**Q1055. Water is flowing at the rate of 5 km/h through a pipe of diameter 14 cm into a rectangular tank which is 50 m long, 44m wide. The time taken, in hours, for the rise in the level of water in the tank to be 7 cm is**

(a) 2 (b)5/2 (c) 3 (d) 5/2

**Q1056. The side of a quadrilateral are in the ratio 3 : 4 : 5 : 6 and its perimeter is 72 cm. The length of its greatest side (in cm) is**

(a) 24 (b) 27 (c) 30 (d) 36

**Q1057. The volume (in cm ^{3}) of rain water that can be collected from 1.5 hectares of ground in a rainfall of 5 cm is**

(a) 75 (b) 750 (c) 7500 (d) 75000

**Q1058. A drum of kerosene is 3/4****full. When 30 litres of kerosene is drawn from it, it remains 7/12**** full. The capacity of the drum is**

(a) 120 ? (b) 135 ? (c) 150 ? (d) 180 ?

**Q1059. The length (in cm) of a chord of a circle of radius 13 cm at a distance of 12 cm from its centre is**

(a) 5 (b) 8 (c) 10 (d) 12

**Q1060. A copper wire is bent in the form of square with an area of 121 cm ^{2}. If the same wire is bent in the form of a circle, the radius (in cm) of the circle is(Take π = 22/7)**

(a) 7 (b) 10 (c) 11 (d) 14

**Q1061. A copper wire is bent in the form of an equilateral triangle and has area 121√3**** cm ^{2}. If the same wire is bent into the form of a circle, the area (in cm^{2}) enclosed by the wire is(Take π = 22/7)**

(a) 364.5 (b) 693.5 (c) 346.5 (d) 639.5

**Q1062. If the length of a rectangular plot of land is increased by 5% and the breadth is decreased by 10%, how much will its area increase or decrease?**

(a) 6.5% increase (b) 5.5% decrease (c) 5.5% increase (d) 6.5% decrease

**Q1063. The radius of base and slant height of a cone are in the ratio 4 : 7. If its curved surface area is 792 cm ^{2}, then the radius (in cm) of its base is (Use **

**π= 22/7)**

(a) 8 (b) 12 (c) 14 (d) 16

**Q1064. The area of a right-angled isosceles triangle having hypotenuse 16**** cm is**

(a) 144 cm^{2} (b) 128 cm^{2} (c) 112 cm^{2} (d) 110 cm^{2}

**Q1065. The ratio of the radii of two wheels is 3 : 4. The ratio of their circumferences is**

(a) 4 : 3 (b) 3 : 4 (c) 2 : 3 (d) 3 : 2

**Q1066. A right circular cylinder just encloses a sphere of radius r. The ratio of the surface area of the sphere and the curved surface area of the cylinder is**

(a) 2 : 1 (b) 1 : 2 (c) 1 : 3 (d) 1 : 1

**Q1067. If each of the radius of base and height of a right circular cone is increased by 10%, then the percentage of increase in the volume of the cone will be**

(a) 20 (b) 33.1 (c) 44.2 (d) 100

**Q1068. The ratio of the areas of two isosceles triangles having equal vertical angles is 1: 4. The ratio of their heights will be**

(a) 1 : 2 (b) 3 : 4 (c) 2 : 3 (d) 6 : 7

**Q1069. The area of an equilateral triangle, inscribed in a circle, is 4√3**** cm ^{2}. The area of the circle is terms of π**

**will be**

(a) 4√6 π (b) 5π (c) 5 1/3π (d) 6π

**Q1070. If each side of a square is increased by 10% what is the percentage of increase of the area?**

(a) 10 (b) 21 (c) 42 (d) 100

**Q1071. If the length of a rectangle is increased by 10% and its breadth is decreased by 10%, the change in its area will be**

(a) 1% increase (b) 1% decrease (c) 10% increase (d) No change

**Q1072. Two solid cylinders of radii 4 cm and 5cm and lengths 6 cm and 4cm respectively are recast into cylindrical disc of thickness 1 cm. The radius of the disc is**

(a) 7 cm (b) 14 cm (c) 21 cm (d) 28 cm

**Q1073. An equilateral triangle of side 6 cm has its corners cut off to form a regular hexagon. Area (in cm ^{2}) of his regular hexagon will be**

(a) 3√3 (b) 3 √6 (c) 6√3 (d)5√3/2

**Q1074. The largest sphere is carved out of cube of side 7 cm. The volume of the sphere (in cm ^{3}) will be**

(a) 718.66 (b) 543.72 (c) 481.34 (d) 179.67

**Q1075. If each side of a square is increased by 10%, its area will be increased by**

(a) 10% (b) 21% (c) 44% (d) 100%

**Q1076. If the circumference of a circle is decreased by 50% then the percentage of decrease in its area is**

(a) 25 (b) 50 (c) 60 (d) 75

**Q1077.The length (in metres) of the longest rod that can be put in a room of dimensions 10 m ×**** 10 m×10m×5m is**

(a) 15√3 (b) 15 (c) 10√2 (d) 5√3

**Q1078. What part of a ditch, 48 metres long 16.5 metres broad and 4 metres deep can be filled by the earth got by digging a cylindrical tunnel of diameter 4 metres and length 56 metres?(**

(a) 1/9 (b) 2/9 (c)7/9 (d)8/9

**Q1079. Volume of two cones are in the ratio 1 : 4 and their diameters are in the ratio 4 : 5. The ratio of their heights is**

(a) 1 : 5 (b) 5 : 4 (c) 5 : 16 (d) 25 : 64

**Q1080. The radius of circle A is twice that of circle B and the radius of circle B is twice that of circle C. Their area will be in the ratio**

(a) 16 : 4 : 1 (b) 4 : 2 : 1 (c) 1 : 2 : 4 (d) 1 : 4 : 16

**Q1081. The sides of a triangle are 6 cm, 8 cm and 10 cm. The area of the greatest square that can be inscribed in it, is**

(a) 18 cm^{2} (b) 15 cm^{2} (c) 2304/49 cm^{2} (d)576/50 cm^{2}

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